Worked Estimand Analysis for a Discontinuation Trial

Why Discontinuation Changes the Question

In a randomized trial, some participants stop their assigned treatment before the endpoint is measured. That event does not by itself determine what the trial’s treatment effect means. If the question concerns the effect of assignment under the treatment use that actually follows, outcomes after discontinuation are part of the answer. If the question instead concerns what would happen if participants did not discontinue, the target is a different, hypothetical effect.

The distinction matters clinically. A treatment-policy effect can describe the consequence of assigning a treatment strategy that includes the discontinuation and subsequent care observed in the trial. A hypothetical effect can address the effect under a specified scenario in which discontinuation is prevented. Neither is universally preferable: the relevant target depends on the clinical question.

For precision, let \(Y^a\) denote the endpoint that would be observed under assignment \(a\), allowing discontinuation and subsequent care to follow the trial’s treatment-policy conditions. Let \(Y^{a,\mathrm{ND}}\) denote the endpoint under assignment \(a\) in the specified hypothetical scenario of no discontinuation. For a mean difference defined as experimental minus control, the targets are

The population, endpoint, time point, and contrast scale must be the same when comparing these two targets. The hypothetical scenario also needs a clinical definition: for example, participants continue their assigned treatment through week 24. “No discontinuation” is not sufficiently precise if it leaves unclear what treatment is continued or how other events are handled. The treatment-policy target likewise needs clarity about subsequent care: it includes the consequences of discontinuation and any specified post-discontinuation treatment practices.

What Post-Discontinuation Outcomes Contribute

For the treatment-policy estimand, an endpoint measured after discontinuation is still an outcome for the randomized participant. It reflects the participant’s course after assignment, including discontinuation and any subsequent care. Using that outcome preserves the target’s focus on assignment rather than restricting the analysis to participants who remained on treatment. If the endpoint is not collected, that is a missing-outcome problem; discontinuation and missingness are not interchangeable.

For the hypothetical estimand, the observed endpoint after discontinuation is generally not the endpoint under continued assigned treatment. It may inform a model, but it does not directly reveal \(Y^{a,\mathrm{ND}}\). Estimation therefore requires assumptions connecting observed data to the unobserved hypothetical outcomes. Randomization alone identifies contrasts between assignment groups under their observed treatment policies; it does not, by itself, identify what would have happened had discontinuation been prevented.

Calculating a Treatment-Policy Contrast

Suppose \(Y\) is observed for everyone at the endpoint and the randomized groups are analyzed as assigned. Under randomization, consistency of the observed outcome with the assigned strategy, and complete endpoint ascertainment, the mean outcome in each assignment group estimates the corresponding treatment-policy mean. The justification is that randomization makes assignment independent of the potential outcomes, while consistency gives \(Y=Y^a\) for a participant assigned \(a\). Thus \(E(Y\mid A=a)=E(Y^a)\).

The last equality is an estimation statement for the sample contrast, not a claim that every observed sample contrast equals the population effect. Sampling uncertainty remains. If outcomes are missing, the group means of observed outcomes alone do not automatically estimate the target; assumptions or methods for missing outcomes are needed. The earlier material on Missing Data Within a Defined Estimand treats that separate issue.

Estimating a Hypothetical No-Discontinuation Effect

A direct estimate of the hypothetical target is not available merely by comparing observed outcomes among participants who continued. To illustrate one possible identification argument, let \(L\) denote measured characteristics that predict both discontinuation and the outcome, and consider a simplified setting with one such baseline stratification variable. Suppose the conditional mean outcome under no discontinuation can be estimated among participants who remain on assigned treatment. A standardization calculation averages those conditional means over the baseline distribution of the full randomized population, not just the continuers.

This calculation relies on substantive assumptions. The hypothetical intervention and continued treatment must be well defined; consistency must connect observed outcomes under continued assigned treatment to the corresponding hypothetical outcomes; within assignment and \(L\), observed continuers must be comparable to all participants with respect to their potential outcomes under no discontinuation; and there must be continuers at each relevant value of \(L\) (positivity). The conditional mean model must also be adequate. If evolving symptoms, adverse effects, or other time-varying factors predict both discontinuation and outcome, a baseline-only adjustment may not make continuers comparable. These assumptions are not guaranteed by randomization.

under the stated assumptions. This is a standardization identity: use the estimated conditional mean for each baseline stratum, then weight it by that stratum’s proportion in the target population. The formula is not justified if the comparability, positivity, consistency, or model conditions fail.

Diagnostics, Alternatives, and Limitations

Before interpreting either analysis, check whether it matches the estimand. For a treatment-policy analysis, verify that participants were analyzed by randomized assignment and that outcomes after discontinuation were retained when collected. Report how many outcomes were not collected in each group and distinguish those missing outcomes from discontinuation itself. For a hypothetical analysis, inspect whether relevant predictors of discontinuation and outcome were measured, whether continued participants exist across the covariate patterns used for prediction, and whether model predictions are plausible. Sparse or empty strata signal a positivity problem; extreme predictions or strong sensitivity to model choices can indicate poor support or misspecification.

The main alternative is not simply another calculation on the same endpoint: it is a different estimand. Treatment-policy analysis uses the observed post-discontinuation course and answers an assignment-strategy question. Hypothetical analysis targets an intervention scenario that may be clinically informative but depends on assumptions about unobserved outcomes. A while-on-treatment summary, which uses outcomes only while participants remain on treatment, answers yet another question and can be affected by selection into continued treatment. These approaches should not be presented as interchangeable estimates of one effect.

Neither target automatically handles every complication. A treatment-policy estimand does not make missing endpoint data disappear; a hypothetical estimand does not become identified just because the trial was randomized. Estimates also depend on the endpoint definition, timing, population, and handling of other intercurrent events. State these features alongside the numerical contrast so readers can tell what clinical question the result addresses.

A Common Mistake